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PaperTest GMAT - Percent problem

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PaperTest GMAT - Percent problem

by oks » Tue Sep 02, 2008 9:52 pm
In year Y imported machine tools accounted for 25% of total machine-tool sales in the US, and Japanese imports accounted for 45% of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the US was how many billion dollars?

Answer: 80x/9

I used the plug in "smart" numbers approach and arrived at the correct answer. However, this is time consuming. Is there a faster way to solve this problem?

thanks!
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by loki.gmat » Tue Sep 02, 2008 11:36 pm
let U = total sales of all machine tools in the US
& Y = imported machine tools which accounted for 25% of total machine-tool sales in the US

x = Japanese imports (given)

from given data we have
Y = U/4

& (45/100)/(U/4) = x

solving we get U = 80*x/9


Thanks!
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by canuckclint » Wed Sep 03, 2008 4:00 pm
Let t be total.

Then t (45/100) (25/100) = x
or
t (45/100) (1/4) = x
x = 400/45

Simplifying you arrive at the answer!
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